Integrability of a Generalized Ito System: the Painleve Test

It is shown that a generalized Ito system of four coupled nonlinear evolution equations passes the Painleve test for integrability in five distinct cases, of which two were introduced recently by Tam, Hu and Wang. A conjecture is formulated on integrability of a vector generalization of the Ito system.Comment: LaTeX, 5 page

Towards the production of radiotherapy treatment shells on 3D printers using data derived from DICOM CT and MRI: preclinical feasibility studies

Background: Immobilisation for patients undergoing brain or head and neck radiotherapy is achieved using perspex or thermoplastic devices that require direct moulding to patient anatomy. The mould room visit can be distressing for patients and the shells do not always fit perfectly. In addition the mould room process can be time consuming. With recent developments in three-dimensional (3D) printing technologies comes the potential to generate a treatment shell directly from a computer model of a patient. Typically, a patient requiring radiotherapy treatment will have had a computed tomography (CT) scan and if a computer model of a shell could be obtained directly from the CT data it would reduce patient distress, reduce visits, obtain a close fitting shell and possibly enable the patient to start their radiotherapy treatment more quickly. Purpose: This paper focuses on the first stage of generating the front part of the shell and investigates the dosimetric properties of the materials to show the feasibility of 3D printer materials for the production of a radiotherapy treatment shell. Materials and methods: Computer algorithms are used to segment the surface of the patient’s head from CT and MRI datasets. After segmentation approaches are used to construct a 3D model suitable for printing on a 3D printer. To ensure that 3D printing is feasible the properties of a set of 3D printing materials are tested. Conclusions: The majority of the possible candidate 3D printing materials tested result in very similar attenuation of a therapeutic radiotherapy beam as the Orfit soft-drape masks currently in use in many UK radiotherapy centres. The costs involved in 3D printing are reducing and the applications to medicine are becoming more widely adopted. In this paper we show that 3D printing of bespoke radiotherapy masks is feasible and warrants further investigation

A Survey of 56 Mid-latitude EGRET Error Boxes for Radio Pulsars

We have conducted a radio pulsar survey of 56 unidentified gamma-ray sources from the 3rd EGRET catalog which are at intermediate Galactic latitudes (5 deg. < |b| < 73 deg.). For each source, four interleaved 35-minute pointings were made with the 13-beam, 1400-MHz multibeam receiver on the Parkes 64-m radio telescope. This covered the 95% error box of each source at a limiting sensitivity of about 0.2 mJy to pulsed radio emission for periods P > 10 ms and dispersion measures < 50 pc cm-3. Roughly half of the unidentified gamma-ray sources at |b| > 5 deg. with no proposed active galactic nucleus counterpart were covered in this survey. We detected nine isolated pulsars and four recycled binary pulsars, with three from each class being new. Timing observations suggest that only one of the pulsars has a spin-down luminosity which is even marginally consistent with the inferred luminosity of its coincident EGRET source. Our results suggest that population models, which include the Gould belt as a component, overestimate the number of isolated pulsars among the mid-latitude Galactic gamma-ray sources and that it is unlikely that Gould belt pulsars make up the majority of these sources. However, the possibility of steep pulsar radio spectra and the confusion of terrestrial radio interference with long-period pulsars (P > 200 ms) having very low dispersion measures (< 10 pc cm-3, expected for sources at a distance of less than about 1 kpc) prevent us from strongly ruling out this hypothesis. Our results also do not support the hypothesis that millisecond pulsars make up the majority of these sources. Non-pulsar source classes should therefore be further investigated as possible counterparts to the unidentified EGRET sources at intermediate Galactic latitudes.Comment: 24 pages, including 4 figures and 3 tables. Accepted for publication in Ap

Metal-Insulator-Transition in a Weakly interacting Disordered Electron System

The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, non-local cluster self-energy ($\Sigma_c[{\cal \tilde{G}}](i,j\neq i)$) up to second order in the perturbation expansion of interactions, $U^2$, with a systematic incorporation of non-local spatial correlations and diagonal disorder, we explore the initial effects of electron interactions ($U$) in three dimensions. We find that the critical disorder strength ($W_c^U$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate $W$ close to $W_c^U$ and demonstrate that the mobility edge ($\omega_\epsilon$) is preserved as long as the chemical potential, $\mu$, is at or beyond the mobility edge energy.Comment: 10 Pages, 8 Figures with Supplementary materials include

Finite Cluster Typical Medium Theory for Disordered Electronic Systems

We use the recently developed typical medium dynamical cluster (TMDCA) approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the proper characterization of the localization transition in all the disorder distributions studied. As a function of increasing cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge for disorder distributions with finite variance, obtaining the correct critical disorder strengths, and shows that the order parameter critical exponent for the Anderson localization transition is universal. The TMDCA is computationally efficient, requiring only a small cluster to obtain qualitative and quantitative data in good agreement with numerical exact results at a fraction of the computational cost. Our results demonstrate that the TMDCA provides a consistent and systematic description of the Anderson localization transition.Comment: 20 Pages, 19 Figures, 3 Table

Critical property of spin-glass transition in a bond-disordered classical antiferromagnetic Heisenberg model with a biquadratic interaction

Motivated by puzzling spin-glass behaviors observed in many pyrochlore-based magnets, effects of magnetoelastic coupling to local lattice distortions were recently studied by the authors for a bond-disordered antiferromagnet on a pyrochlore lattice [Phys. Rev. Lett. 107, 047204 (2011)]. Here, we extend the analyses with focusing on the critical property of the spin-glass transition which occurs concomitantly with a nematic transition. Finite-size scaling analyses are performed up to a larger system size with 8192 spins to estimate the transition temperature and critical exponents. The exponents are compared with those in the absence of the magnetoelastic coupling and with those for the canonical spin-glass systems. We also discuss the temperature dependence of the specific heat in comparison with that in canonical spin-glass systems as well as an experimental result.Comment: 4 pages, 2 figures, proceedings for LT2

Vortices and the entrainment transition in the 2D Kuramoto model

We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase ($K>K_E$), vortices move in fixed paths around clusters, while in the unentrained phase ($K<K_E$), vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling $K_E\sim K_L$ for small lattices, where $K_L$ is the threshold for phase-locking. By also deriving the scaling $K_L\sim\log N$, we thus show that $K_E\sim\log N$ for small $N$, in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated.Comment: 11 pages, 8 figure